Denying the antecedent
Denying the antecedent is a type of logical fallacy.
Suppose in an argument one were to deny the "if" part of a conditional (the antecedent) first, and conclude with the denial of "then" part (the consequent).
- If P, then Q.
- P is false.
- Therefore, Q is false.
This argument form has the name denying the antecedent, because in arguing this way one does indeed deny the antecedent in the second premise. This is a logical fallacy. If we argue this way, we make a mistake. One can see this with an example:
- If there is fire here, then there is oxygen here. (Since oxygen is required for fire.)
- There is no fire here.
- Therefore, there is no oxygen here.
See also: modus ponens, modus tollens, affirming the consequent.
